You didn't say if Federal or State, so I'll tell you about Federal payments by credit card. State payment options can vary.
You can pay Federal taxes due by credit card at the IRS website, but be sure you really want to pay by that method. The service fee can be hefty no matter where paid. I believe around 2%. I'm not exactly sure what it is in when paid through the TurboTax program. It goes to a third-party processor, so I suspect the service fee is at least that much. In any case, when paying by credit card, if you have a large tax bill, the service fee can be high.
In any case, to pay by credit card at the IRS website, here's how to go there, where you can choose from several processing companies that the IRS lists as well as their fees:
https://www.irs.gov/payments
When you choose the credit/debit card option, the next page will show you several processors and what their fees are.
The IRS also has "Direct Pay" at that same link where you can pay for free by using electronic debit of your bank account.
@tommoon23
I corrected a typo above, but you have been emailed the original answer. I mistyped that I was going to tell you about State, when I meant to say I was going to tell you in regards to Federal. I've corrected that above.
If you need info on paying state taxes by credit card, you can look it up on your state tax agency's website, where they should have a FAQ or instruction on how to pay state taxes due, or they may even have a portal to make the payment on their website.
Thanks, on Turbo tax, they didn't give me an option to "NOT" pay through them so I clicked "pay by check" but paid through the IRS site. (IRS site has lower credit card fees than Turbo Tax). Would this be okay?
Yes, that is how one proceeds to pay by another method somewhere else. You choose "pay by check" then you are free to pay by any method you wish. I have chosen that "check" option before and then paid from my bank account later. The IRS doesn't care as long as they get their money before the filing deadline.
By the way, what was the percentage service fee TurboTax affiliated payment processor was going to charge you?